Abstract

The classes of lower-C1,αC^{1,\alpha} functions (0<α≤10<\alpha\leq 1), that is, functions locally representable as a maximum of a compactly parametrized family of continuously differentiable functions with α\alpha-Hölder derivative, are hereby introduced. These classes form a strictly decreasing sequence from the larger class of lower-C1C^1 towards the smaller class of lower-C2C^2 functions, and can be analogously characterized via perturbed convex inequalities or via appropriate generalized monotonicity properties of their subdifferentials. Several examples are provided and a complete classification is given.

Author information

Contact details are reproduced from the original publication and may be historical.

Aris Daniilidis

Dep. de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

arisd@mat.uab.es

Jérôme Malick

INRIA, Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, St. Martin, 38334 Saint Ismier, France

jerome.malick@inria.fr

Keywords

  • Maximum function
  • lower-C1,α function
  • α-weakly convex function
  • α-hypomonotone operator

Mathematics Subject Classification

26B25; 49J52, 47H05

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Suggested citation

A. Daniilidis, J. Malick. “Filling the Gap between Lower-C^1 and Lower-C^2 Functions.” Journal of Convex Analysis 12 (2005), No. 2, 315–329. https://doi.org/10.68381/jca12022

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press.